4. 2D Kinematics

A football at rest is kicked by a football kicker. The ball is in contact with the kicker's foot for 0.050s, during which it experiences an acceleration a = 340 m/s². The ball is launched at an angle of 40° above the ground (x-axis). Calculate the horizontal and vertical components of the launch velocity.

A car is moving with speed 16.0 m/s due south at one moment and 25.7 m/s due east 8.00 s later. Over this time interval, determine the magnitude and direction of (a) its average velocity, (b) its average acceleration. (c) What is its average speed? [Hint: Can you determine all these from the information given?]

A remote-controlled car is moving in a vacant parking lot. The velocity of the car as a function of time is given by $\vec{v} = \left[ 5.00~\mathrm{m/s} - (0.0180~\mathrm{m/s^3})t^2 \right] \hat{i} + \left[ 2.00~\mathrm{m/s} + (0.550~\mathrm{m/s^2})t \right] \hat{j}$. What are the magnitude and direction of the car's velocity at $t=8.00s$? (b) What are the magnitude and direction of the car's acceleration at $t=8.00s$?

The coordinates of a bird flying in the xy-plane are given by x(t) = αt and y(t) = 3.0 m − βt², where α = 2.4 m/s and β = 1.2 m/s². Calculate the magnitude and direction of the bird's velocity and acceleration at t = 2.0 s.

Complete the motion diagram by adding acceleration vectors.

A rocket-powered hockey puck moves on a horizontal frictionless table. Figure EX4.7 shows graphs of v_x and v_y the x- and y-components of the puck's velocity. The puck starts at the origin. What is the magnitude of the puck's acceleration at t = 5s?

(II) On mountainous downhill roads, an escape lane is sometimes placed to the side of the road for trucks whose brakes might fail. Assuming a constant upward slope of 26°, calculate the horizontal and vertical components of the acceleration of a truck that slowed from 110 km/h to rest in 7.0 s. See Fig. 3–43.

A diver running 2.5 m/s dives out horizontally from the edge of a vertical cliff and 3.5 s later reaches the water below. How high was the cliff and how far from its base did the diver hit the water?

(II) A ball thrown horizontally at 10.8 m/s from the roof of a building lands 21.0 m from the base of the building. How high is the building?

A remote-controlled car is moving in a vacant parking lot. The velocity of the car as a function of time is given by $\vec{v} = \left[ 5.00~\mathrm{m/s} - (0.0180~\mathrm{m/s^3})t^2 \right] \hat{i} + \left[ 2.00~\mathrm{m/s} + (0.550~\mathrm{m/s^2})t \right] \hat{j}$. What are $a_x\left(t\right)$ and $a_y\left(t\right)$, the $x$- and $y$- components of the car's velocity as functions of time?